Post on 27-Oct-2021
Ray-tracing Traveltime Tomography vs Wave-equation
Traveltime Inversion for Near-Surface Seismic Land Data
Journal: Interpretation
Manuscript ID INT-2016-0210.R2
Manuscript Type: 2016-05 Skeletonized/sparse/multiscale geophysical inversion for the interpreter
Date Submitted by the Author: 13-Apr-2017
Complete List of Authors: Fu, Lei; King Abdullah University of Science and Technology, Earth Science and Engineering Program Hanafi, Sherif; KAUST, Earth Science
Keywords: head waves, water table, traveltime
Subject Areas:
Application examples (applying a relatively new technique or concept),
Near-surface, ground penetrating radar, environmental, and engineering applications
Note: The following files were submitted by the author for peer review, but cannot be converted to PDF. You must view these files (e.g. movies) online.
INT_WT_final _table.tex
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Ray-tracing Traveltime Tomography vs
Wave-equation Traveltime Inversion for
Near-Surface Seismic Land Data
Lei Fu1∗, Sherif M. Hanafy1,2
1Division of Physical Science and Engineering, King Abdullah University of Science
and Technology (KAUST),Thuwal, Saudia Arabic
2Geophysics Departmen, Cairo University, Cairo, Egypt
Corresponding author: Lei Fu (lei.fu@kaust.edu.sa)
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ABSTRACT
Full waveform inversion (FWI) of land seismic data tends to get stuck in the
local minima associated with the waveform misfit function. This problem can be
partly mitigated by using an initial velocity model that is close to the true velocity
model. This initial starting model can be obtained by inverting traveltimes with
ray-tracing traveltime tomography (RT) or wave-equation traveltime inversion
(WT). We now show that WT can provide a more accurate tomogram than RT
by inverting the first-arrival traveltimes, and RT is more sensitive to the additive
noise in the input data than WT. We present two examples of applying WT and
RT to land seismic data acquired in western Saudi Arabia. One of the seismic
experiments investigated the water-table depth, and the other one attempted to
detect the location of a buried fault. The seismic land data were inverted by WT
and RT to generate the P-velocity tomograms, from which we can clearly identify
the water table depth along the seismic survey line in the first example and the
fault location in the second example.
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INTRODUCTION
For land seismic surveys, the near-surface velocity model is important for comput-
ing an accurate migration image (Vermeer, 2002). The near-surface velocity model
is obtained by traveltime tomography which inverts the first-arrival traveltimes for
the P-velocity model. These arrivals are those of either diving waves or refractions.
Ray-tracing traveltime tomography (RT) has been used for earthquake imaging of the
earth’s interior from the early 1970s (Aki et al., 1977; Humphreys et al., 1984), which
was mostly implemented using the high-frequency approximation of ray tracing to
calculate the traveltimes. To avoid the high-frequency assumption of RT, Luo and
Schuster (1991a,b) proposed a wave-equation traveltime inversion (WT) method to
obtain the near-surface P-wave velocity model. The WT method can be more accu-
rate than RT, but it is at least an order-of-magnitude more costly because the wave
equation must be numerically solved for each source.
Full wave inversion (FWI) is an underdetermined problem, where many different
models yield synthetic data that match observed data within a reasonable tolerance.
The local minima and cycle-skipping problems in FWI are partly caused by an in-
accurate estimate of the source wavelet, an inaccurate amplitude modeling, elastic
effects, random noise and an inaccurate initial velocity model. In order to suppress
the source wavelet effect, Frazer and Sun (1998) developed a source-independent algo-
rithm using convolved wavefields. Bai et al. (2014) presented visco-acoustic waveform
inversion in the time domain for velocity estimation, where visco-acoustic wave equa-
tions are used to generate accurate amplitudes. To reduce the harmful effects of noise
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in the data, Neelamani et al. (2008) applied a curvelet-based algorithm to attenuate
random and coherent linear noise in a 3D data set from a carbonate environment.
To partly migrate the local minima problem of FWI, Yu and Hanafy (2014) applied
a multiscale early arrival waveform inversion (MEWI, which gradually lengthens the
time window for muting early arrivals ) to shallow seismic land data. However, an ac-
curate initial velocity model is very important for obtaining an accurate tomogram in
both MEWI and FWI. Both WT and RT inversion methods can provide a reasonable
initial velocity model. However, WT (Luo and Schuster, 1991b) does not require a
high-frequency assumption and can account for body-wave, diffraction, reflection and
headwave traveltimes. Hence, the WT (Luo and Schuster, 1991a,b) method should
provide a more accurate initial velocity model than the RT method for MEWI or
FWI.
In this paper, one synthetic and two field data examples are used to demonstrate
the advantages of WT over the RT method. We first describe the theory of the
WT and RT methods, and then describe how WT and RT is implemented using a
workflow. We then present the numerical results for applying both WT and RT to
one synthetic and two field data examples. The final section presents the discussion
and conclusions.
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WAVE-EQUATION TRAVELTIME INVERSION
For seismic data, refraction waves can be modeled by solving the 2D constant-density
acoustic wave equation (Yilmaz, 2001)
∇2p(x, t)− 1
∂t2 = f(x, t), (1)
where, x is the model space, ∇2=
(
∂∂x
2 ,∂
∂y2
)
is the 2D Laplacian, v(x) is the P-wave
velocity model, p(x, t) is the pressure field, and f(x, t) is the source term. The wave-
equation traveltime inversion (WT) method is designed to minimize the following
objective function:
Φ(v) =1
2‖∆τrs‖2, (2)
where, v is the P-wave velocity, ∆τrs = τcal(xr,xs) − τobs(xr,xs) is the refraction
traveltime residual for a source at xs and a receiver at xr (Luo and Schuster, 1991b,a).
In practice, the traveltime difference can be found by cross-correlating the predicted
and the observed seismograms (Luo and Schuster, 1991b). The P-velocity distribution
can be iteratively updated using any gradient-based method (Scales, 1985) such as
the conjugate gradient method:
vk+1 = vk + αkdk, (3)
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where vk+1 is the P-velocity model at the (k+1)th iteration; αk is the scale step length,
which can be found using a line-search algorithm; and dk is the updated direction:
dk = −gk + βkdk−1, (4)
βk =(gk − gk−1, gk)
∂vk
and the former search direction dk−1. Since WT is a non-linear inversion method, we
use a quadratic line search method to compute the step length (Wright and Nocedal,
1999). Several reasonable values of the step length are selected, e.g., α1 = 0.5 and
α2 = 1, and the objective functions Φ(vk + α1dk) and Φ(vk + α2dk) are computed
to determine if they are less than Φ(vk), and if Φ(vk + α1dk) < Φ(vk + α2dk). Then
the following quadratic formula is used to determine the interpolated value of the
objective function,
Φ(vk + αdk) =(α−α1)(α−α2)
α1α2 Φ(vk) +α(α−α2)
α1(α1−α2)Φ(vk + α1dk)
+α(α−α1)
α2(α2−α1)Φ(vk + α2dk) 0 ≤ α ≤ α2. (6)
The scalar value α is found by differentiating Φ(α) of equation 6 with respect to α,
setting the result to zero, and solving for α (see Schuster (2017) for further details).
In wave-equation traveltime inversion, the gradient of the misfit function with
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respect to the P-wave velocity is given by (Luo and Schuster, 1991b)
g =1
8
Ray-tracing Traveltime Tomography
The Ray-tracing traveltime tomography is based on the idea that the traveltime of a
ray is the discretized integral of the slowness along the ray:
ti =N∑
j=1
lijsj, (9)
where ti is the traveltime of the ith ray, lij is the segment length of the ith ray that
intersects the jth cells, sj is the slowness (reciprocal velocity) in the jth cell. This
results in anM×N system of equations, denoted in matrix-vector notation as Ls = t,
where t represents the recorded M × 1 traveltime data vector, and s is the N × 1
vector of unknown slownesses in the N cells. The M × N matrix L contains the
segment lengths of the rays.
The least-squares solution of equation 9 is by minimizing the following objective
function:
ǫ =1
2
M∑
i=1
N∑
j=1
(lijsj − ti)2,
=1
2
M∑
i=1
r2i , (10)
where ri =∑
j(lijsj − ti) is the ith
traveltime residual between the predicted and
observed ith
traveltimes. If the rays bend then the matrix elements (lij) depend on
the unknowns sj . In this case the traveltime equations are non-linear and so that
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the rays must be recomputed for the new slowness model after each iteration. The
slowness s can be iteratively updated using the conjugate gradient method:
sk+1 = sk + αkdk, (11)
where sk+1 is the slowness at the (k + 1)th iteration, αk is the scale step length, dk
is the updated direction determined by the derivative ∂ǫ
sk , k = 0) is given.
3. The first-arrival traveltimes (τcal) are calculated using the given initial velocity
model.
4. If the RMS error between the observed and calculated traveltimes (τobs − τcal)
is larger than a predefined tolerance (a quarter of the dominant period ), then
the velocity model is updated.
5. Steps 3 and 4 are iteratively repeated until the RMS traveltime error is less
than the given tolerance.Page 9 of 34
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NUMERICAL RESULTS
The WT and RT methods are now tested on one synthetic and two data sets recorded
over the western side of Saudi Arabia. One of the seismic surveys was carried out at
Wadi Qudaid for the purpose of determining the water-table depth. The other survey
was carried out near the Gulf of Aqaba to detect the location of a hidden fault.
Synthetic Example
The synthetic P-velocity model we created is shown in Figure ??a, which is a complex
model with an irregular interface. It is discretized into 60 x 300 grid-points with the
grid size of 1.5 m. A finite-difference solution to the 2D acoustic wave equation is
used to compute 60 shot gathers with 60 geophones evenly deployed on the surface
with a 7.5 m interval. The source wavelet is a Ricker wavelet with a peak frequency
of 50 Hz. The goal of this synthetic test is to show that the WT method is more
accurate than the RT method when the high-frequency assumption of RT is violated.
This violation occurs when the characteristic wavelength 1 of the velocity model is
about the same or less than the dominant wavelength of the refraction wavefield (Luo
and Schuster, 1991b).
The initial velocity model is the gradient velocity model shown in Figure ??b.
The traveltimes of the first arrivals are picked and inverted, and the resulting WT
and RT tomograms are shown in Figures ??c and ??d, respectively. The dashed
11
yellow and white lines denote the value of 1550 m/s and 1800 m/s respectively in the
actual tomogram, and are used as the reference markers for the tomograms. In this
regard, the WT tomogram is closer to the true model than the RT tomogram.
The horizontal velocity profiles at the depth of 25 m are shown in Figure ??, where
the black, blue, green and red curves represent the velocity of the true model, initial
model, RT tomogram, and WT tomogram. We can see that the velocity profile from
the WT tomogram is more accurate than the RT profile. This suggests that the WT
method can provide a much more accurate velocity model than the RT method when
the high-frequency assumption is violated.
Table 1 shows the computational metrics for the WT and RT methods. The root
mean square (rms) traveltime differences for WT and RT are 5.1 ms and 5.8 ms at
the final iteration, respectively. The WT method is 120 times more computation-
ally expensive than the RT method, when those codes are executed with a 12-core
workstation.
To test the noise sensitivity of these methods, 10% random noise is added to the
raw wiggle traces for WT, and 10% random noise is added to the picked traveltimes
for RT. The corresponding WT and RT tomograms with the noisy data are shown
in Figures ??e and ??f, respectively. We can see that the WT tomogram with noise
(??e) is almost the same as the WT tomogram without noise (??c), while the RT
tomogram with noise (??f) is different from the RT tomogram without noise (??d),
which means that the RT is more sensitive to the level of noise in the input data.
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Data Processing for Field Data
The first-arrival traveltimes are manually picked, and a reciprocity test 2 is applied to
reject the traveltimes with a picking errors larger than one quarter of the dominant
period. Then the traveltimes are used for the input data for RT. For WT inversion,
in order to suppress elastic effects such as surface waves, and account for geometrical
spreading, the seismic land data are processed by the following steps:
1. We applied a 3D to 2D approximation by multiplying the trace spectrum by
√
t in the time
domain.
3. The traces are windowed to only admit the first-arrival refraction events.
4. The traces recorded within one dominant wavelength from the source are muted
because they contain surface waves and noise even after filtering.
Wadi Qudaid Field Data
A seismic survey was carried out at Wadi Qudaid ( red box in Figure ??a). The survey
line is indicated by the double blue arrow, where 117 vertical-component geophones
are deployed at 2.0 m intervals along the survey line. A 90-kg accelerated-weight drop
(Figure ??e) is used as the source at every geophone position to record 117 common
2Reciprocity means that the traveltime from the shot location to the receiver location
should be the same as the traveltime from the receiver location to the shot location.
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shot gathers (CSG). A water well near the study area shows that the near-surface
sediments consist of two layers above the water table. The first layer is composed of
gravel and sand with a thickness of less than 5 m (Figure ??c), the second layer is
composed of sand and silt with some gravel with a thickness of around 10 - 15 m, and
the water table is around 18 m in depth (Figure ??d).
CSG #30 is shown in Figure ??a, where the air, Rayleigh and refraction arrivals
are marked. In our study, we only focus on the refraction arrivals, so all other events
are muted (Figure ??b) and the result is used as the input to the WT inversion. The
WT method can also be extended to inverting the traveltimes of reflection arrivals
Zhang et al. (2011).
The initial model for WT is a velocity-gradient model, which is discretized into
160 x 928 grid-points with the grid size of 0.25 m. The RT, WT, and interpreted WT
tomograms are shown in Figures ??a, ??b, and ??c, respectively. For the near-surface
zone from 0 < z < 25 m, both the RT and WT tomograms have a similar velocity
structure, but the depth to the water table in the RT tomogram is deeper than in the
WT tomogram. The black dashed curve (Figure ??c) denotes the estimated water
table according to the velocity contour value of 1550 m/s, which is consistent with
the water well information in Figures ??c and ??d. The RT tomogram shows a high-
velocity local anomaly at 20 < x < 110 m and z > 25 m, which is not the case in the
WT. In the WT tomogram a continuous bedrock interface is shown at 25 < z < 35
m.
Figure ??a displays the traveltimes for shots 15, 65 and 110. The black, red
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and blue curves represent the observed, WT, and RT traveltimes, respectively. We
can see that WT traveltimes are in better agreement with the observed traveltimes.
Figure ??b shows the normalized traveltime misfit functions for the WT and RT
methods. The RT misfit function only decreases to 20% after 30 iterations, however,
the WT misfit function decreases to about 13% after 10 iterations. In this example,
the WT method has a better convergence rate than the RT method.
Aqaba Field Data
A seismic survey was carried out near the Gulf of Aqaba (the black box area in
Figure ??a), where 120 vertical-component geophones are deployed at 2.5 m intervals
along the black double-arrow line in Figure ??b. A 90-kg accelerated-weight drop is
used for a source at every geophone position to record 120 common shot gathers. A
2D resistivity profile is acquired at the same location parallel to the seismic profile.
The acquisition parameters of the resistivity profile are:
1. Number of electric nodes: 64
2. Node interval: 5 m
3. Configuration array: Schlumberger-Wenner
4. Total profile length: 315 m
5. Both seismic and resistivity profiles share the same starting point of the profile
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A sample CSG is shown in Figure ??a. The air, Rayleigh, reflection and refraction
arrivals are indicated in Figure ??a, and a processed CSG is shown in Figure ??b.
The processed CSGs are the input data for the WT method.
We re-arranged the raw CSGs into the common offset gathers (COGs) with differ-
ent offsets. Figure ??a is the zero-offset COG, which shows a continuous horizontal
event. Figures ??b and ??c are the COGs with the offsets of 20 m and 40 m, respec-
tively, where the events are no longer continuous everywhere, especially at x = 145
m (the area indicated by the black dashed ellipse). The time delays of the surface
waves in the distorted area (ellipse in Figures ??b and ??c) implies that the shear
velocity is slower, and suggests the location of a possible fault.
The initial P-velocity model for WT inversion is a gradient velocity model, which
is discretized into 150 x 598 grid-points with the grid size of 0.5 m. The RT and
WT tomograms after 10 iterations are shown in Figures ??a and ??b. Both the RT
and WT tomograms are similar to each other. Both the RT and WT tomograms
suggest the hidden fault location (indicated by the pink ellipse and dashed red line)
is at 125 < x < 145 m, which is consistent with the resistivity tomogram shown in
Figure ??c. However, compared with the RT tomogram (Figures ??a), the bedrock
interface indicated by the black dashed curve in WT tomogram (Figures ??b) is more
consistent with the bedrock interface revealed by the resistivity tomogram (Figures
??c).
The recorded resistivity data were inverted using the Res2DInv software to gen-
erate the resistivity tomogram (Ostrowski et al., 2010) in Figure ??c. Two distinct
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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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layers are visible in the resistivity tomogram, the first layer has resistivity values
ranging from 250 to 500 Ohm.m with the layer thickness ranging between 6 m and
10 m. The second layer extends to the bottom of the section and has low resistivity
values ranging between 10 and 50 Ohm.m, except between offsets 130 m and 145 m,
where the resistivity values appear to increase to about 250 Ohm.m. The location of
the fault is shown on the resistivity tomogram as a vertical anomaly (between offsets
130 and 145 m) with higher resistivity values (250 Ohm.m) shown in Figure ??c.
Figure ??a show the traveltimes for shots 15, 65 and 110. The black, red and
blue curves represent the observed, WT, and RT traveltimes, respectively. We can
see that the WT traveltimes are in better agreement with the observed traveltimes.
Figure ??b shows the normalized misfit functions for the WT and RT methods, The
misfit function for the RT method only decreases to 25% after 30 iterations, however,
the WT misfit function decreases to about 16% after 10 iterations. In this example,
the WT method has a better convergence rate than the RT method.
DISCUSSION AND CONCLUSIONS
The WT and RT methods are applied to one synthetic example and two seismic land
data sets acquired in western Saudi Arabia. The goal of the Wadi Qadid experiment
is to determine the topography of the water table and the goal of the other survey
is to locate the Aqaba fault. The seismic field data sets are carefully processed
using geometrical spreading corrections, shot normalization, window muting along the
first arrivals, and muting near-offset traces. The WT method generates P-velocity
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Interpretation
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960
This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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17
tomograms, from which we can clearly identify the water-table depth in the Wadi
Qudaid experiment, and the fault location in the Aqaba experiment.
Compared to the RT tomogram, the WT tomogram from Wadi Qudaid indicates
a more accurate water-table depth that is consistent with the water-well information.
The WT tomogram from the Aqaba data suggests a more accurate hidden fault
location, which is in closer agreement with the resistivity tomogram. Although the
WT method requires more than an order-of-magnitude more computational time
compared with the RT method, it can provide a more accurate initial velocity model
for MEWI or FWI.
ACKNOWLEDGEMENTS
The research reported in this publication was supported by the King Abdullah Univer-
sity of Science and Technology (KAUST) in Thuwal, Saudi Arabia. We are grateful to
the sponsors of the Center for Subsurface Imaging and Modeling (CSIM) Consortium
for their financial support. For computer time, this research used the resources of the
Supercomputing Laboratory at KAUST and the IT Research Computing Group. We
thank them for providing the computational resources required for carrying out this
work.
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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REFERENCES
Aki, K., A. Christoffersson, and E. S. Husebye, 1977, Determination of the three-
dimensional seismic structure of the lithosphere: Journal of Geophysical Research,
82, 277–296.
Bai, J., D. Yingst, R. Bloor, and J. Leveille, 2014, Viscoacoustic waveform inversion
of velocity structures in the time domain: Geophysics, 79, R103–R119.
Boonyasiriwat, C., G. T. Schuster, P. Valasek, and W. Cao, 2010, Applications of mul-
tiscale waveform inversion to marine data using a flooding technique and dynamic
early-arrival windows: Geophysics, 75, R129–R136.
Frazer, L. N., and X. Sun, 1998, New objective functions for waveform inversion:
Geophysics, 63, 213–222.
Humphreys, E., R. W. Clayton, and B. H. Hager, 1984, A tomographic image of
mantle structure beneath southern california: Geophysical Research Letters, 11,
625–627.
Luo, Y., and G. T. Schuster, 1991a, Wave equation inversion of skeletalized geophys-
ical data: Geophysical Journal International, 105, 289–294.
——–, 1991b, Wave-equation traveltime inversion: Geophysics, 56, 645–653.
Neelamani, R., A. I. Baumstein, D. G. Gillard, M. T. Hadidi, and W. L. Soroka,
2008, Coherent and random noise attenuation using the curvelet transform: The
Leading Edge, 27, 240–248.
Scales, L., 1985, Introduction to non-linear optimization: Springer-Verlag New York,
Inc.
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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; see
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19
Schuster, G. T., 2017, Seismic inversion: SEG Publishing, Tulsa Oklahoma.
Vermeer, G. J., 2002, 3-d seismic survey design: Society of Exploration Geophysicists.
Wright, S., and J. Nocedal, 1999, Numerical optimization: Springer Science, 35,
67–68.
Yilmaz, O., 2001, Seismic data analysis: Processing, inversion, and interpretation of
seismic data: Society of Exploration Geophysicists.
Yu, H., and S. M. Hanafy, 2014, An application of multiscale early arrival waveform
inversion to shallow seismic data: Near Surface Geophysics, 12, 549–557.
Zhang, J., and M. N. Toksoz, 1998, Nonlinear refraction traveltime tomography:
Geophysics, 63, 1726–1737.
Zhang, S., G. Schuster, and Y. Luo, 2011, Wave-equation reflection traveltime inver-
sion, in SEG Technical Program Expanded Abstracts 2011: Society of Exploration
Geophysicists, 2705–2710.
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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FIGURE & TABLE CAPTION
Figure 1: The flow chart for, a) WT inversion, where ∆ǫ for WT is the misfit change
percentage, and we set the tolerance is 0.01, and b) RT inversion, where ∆ǫ for RT
is the RMS residual, and the tolerance we set is a quarter of the dominant period.
Figure 2: a) The true velocity, b) initial-velocity models for both the WT and RT
methods, c) WT, d) RT, e) WT tomograms with 10% random noise, and f) RT tomo-
gram with 10% random noise. For this velocity model, the characteristic horizontal
variation of the velocity is ≈ 20 m along the interface for 25 m < z < 45 m. Thus
the high-frequency assumption of ray tracing is violated for a 50-Hz source wavelet
having a wavelength about 40 m along this interface. The yellow and white dashed
lines represent the velocity of 1550 m/s and 1800 m/s, respectively, in the true model.
Figure 3: The comparison of the WT and RT velocity profiles at the depth of 25
m, where the black, blue, green and red curves represent the true, initial, RT, and
WT velocity. This profile suggests that the WT method is more accurate than the
RT method.
Figure 4: a) Google map shows the location of the Wadi Qudaid experiment, b)
seismic survey line indicated by the blue double-arrow line, c) photograph showing
the first layer composed of gravel and sand, with a thickness less than 5 m, d) a water
well near the study area showing the second layer composed of sand and silt with
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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21
some gravel, with the thickness of about 10-15 m, and the water table is at z = 18
m, and the e) seismic source is excited by a 90-kg accelerated-weight drop.
Figure 5: a) CSG #30, where the air, Rayleigh, and refraction waves are indicated,
and b) the processed CSG where only the refraction waves are extracted and pro-
cessed.
Figure 6: The RT and WT tomograms inverted from the Wadi Qudaid data: a) RT,
b) WT, and c) interpreted WT tomograms. The black dashed curve is the interpreted
water table and the pink dashed curve is the interpreted bedrock interface.
Figure 7: a) The traveltimes for shots 15, 65, 110, where the black, red and blue
curves represent the observed, WT, and RT traveltimes, respectively, and b) the nor-
malized misfit functions for the WT and RT methods.
Figure 8: a) Google map shows the location of the Aqaba survey, b) photo shows
an earthquake scarp (indicated by the red dashed line) on the surface, and the black
arrow indicates the location of the seismic and resistivity survey lines.
Figure 9: a) CSG#1, where the air, Rayleigh, reflection and refraction arrivals are
indicated, and b) the processed CSG, where only the refraction arrivals are extracted
and processed.
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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Figure 10: Common offset gathers for the source-receiver, a) offset = 0 m, b) offset
= 20 m, and c) offset = 40 m.
Figure 11: The tomograms inverted from the Aqaba data: a) RT and b) WT
tomograms, where the pink ellipses indicate possible fault locations and the black
dashed curves represent the bedrock interfaces, c) resistivity tomogram inverted by
Res2DInv, a low-resistivity anomaly is shown at 130 < x < 145 m, where the white
dashed curve represents the bedrock interface.
Figure 12: a) The traveltimes for shots 5, 65, 105, where the black, red and blue
curves are the observed, WT, and RT traveltimes, respectivly. b) The normalized
misfit function for the WT and RT methods.
Table 1: The computational metrics for the WT and RT methods.
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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1. The flow chart for, a) WT inversion, where $\Delta \epsilon$ for WT is the misfit change percentage, and we set the tolerance is 0.01, and b) RT inversion, where $\Delta \epsilon$ for RT is the RMS residual, and
the tolerance we set is a quarter of the dominant period.
190x90mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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2. a) The true velocity, b) initial-velocity models for both the WT and RT methods, c) WT, d) RT, e) WT tomograms with 10\% random noise, and f) RT tomogram with 10\% random noise. For this velocity
model, the characteristic horizontal variation of the velocity is $\approx 20~m$ along the interface for 25 m
$ < z < $ 45 m. Thus the high-frequency assumption of ray tracing is violated for a 50-Hz source wavelet having a wavelength about 40 m along this interface. The yellow and white dashed lines represent the
velocity of 1550 m/s and 1800 m/s, respectively, in the true model.
161x176mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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ight
; see
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/
3. The comparison of the WT and RT velocity profiles at the depth of 25 m, where the black, blue, green and red curves represent the true, initial, RT, and WT velocity. This profile suggests that the WT method is
more accurate than the RT method.
85x69mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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nse
or c
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ight
; see
Ter
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of U
se a
t http
://lib
rary
.seg
.org
/
4. a) Google map shows the location of the Wadi Qudaid experiment, b) seismic survey line indicated by the blue double-arrow line, c) photograph showing the first layer composed of gravel and sand, with a
thickness less than 5 m, d) a water well near the study area showing the second layer composed of sand
and silt with some gravel, with the thickness of about 10-15 m, and the water table is at $z = 18 $ m, and the e) seismic source is excited by a 90-kg accelerated-weight drop.
297x420mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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or c
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ight
; see
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5. a) CSG \#30, where the air, Rayleigh, and refraction waves are indicated, and b) the processed CSG where only the refraction waves are extracted and processed.
148x112mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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lice
nse
or c
opyr
ight
; see
Ter
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of U
se a
t http
://lib
rary
.seg
.org
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6. The RT and WT tomograms inverted from the Wadi Qudaid data: a) RT, b) WT, and c) interpreted WT tomograms. The black dashed curve is the interpreted water table and the pink dashed curve is the
interpreted bedrock interface.
218x311mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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or c
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ight
; see
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t http
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rary
.seg
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7. a) The traveltimes for shots 15, 65, 110, where the black, red and blue curves represent the
observed, WT, and RT traveltimes, respectively, and b) the normalized misfit functions for the WT and RT
methods.
102x54mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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or c
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; see
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8. a) Google map shows the location of the Aqaba survey, b) photo shows an earthquake scarp (indicated by the red dashed line) on the surface, and the black arrow indicates the location of the seismic and
resistivity survey lines.
163x110mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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or c
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; see
Ter
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t http
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9. a) CSG\#1, where the air, Rayleigh, reflection and refraction arrivals are indicated, and b) the processed CSG, where only the refraction arrivals are extracted and processed.
148x114mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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or c
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ight
; see
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10. Common offset gathers for the source-receiver, a) offset = 0 m, b) offset = 20 m, and c) offset = 40 m.
145x145mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
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rary
.seg
.org
/
11. The tomograms inverted from the Aqaba data: a) RT and b) WT tomograms, where the pink ellipses indicate possible fault locations and the black dashed curves represent the bedrock interfaces, c) resistivity tomogram inverted by Res2DInv, a low-resistivity anomaly is shown at $130 < x <145$ m, where the
white dashed curve represents the bedrock interface.
147x161mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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t to
SEG
lice
nse
or c
opyr
ight
; see
Ter
ms
of U
se a
t http
://lib
rary
.seg
.org
/
12. a) The traveltimes for shots 5, 65, 105, where the black, red and blue curves are the observed, WT,
and RT traveltimes, respectivly. b) The normalized misfit function for the WT and RT methods.
95x46mm (300 x 300 DPI)
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Interpretation
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This paper presented here as accepted for publication in Interpretation prior to copyediting and composition. © 2017 Society of Exploration Geophysicists and American Association of Petroleum Geologists.
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bjec
t to
SEG
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or c
opyr
ight
; see
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ms
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se a
t http
://lib
rary
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.org
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